Abstract—The four index transportation problem (4ITP: origin, destination, goods type, vehicle type) is an extension of the Hitchcock problem, a problem best suited for the goods allocation planning in the case for using the shuttle type. Based on the research results in 1979, in 2011, we developed an exact method for fully solving the 4ITP with determinist parameters. However, because of the limitation of human in recognizing the imprecise natural events in the decision making science, it is necessary to use fuzzy numbers for uncertain condition. By extending the problem toward this direction, in this paper, we develop a method, an extension of fuzzy programming, solving the 4ITP when all parameters such as the cost coefficients, the supply and demand quantities, the goods type and vehicle type quantities are fuzzy numbers and obey the Gaussian law in order 2. We use Gauss method in the fuzzy programming to obtain the costs under form of point cloud. From these results, we use Pham’s method, a method for the conventional 4ITP, to obtain a point cloud with the agglomerating costs. By using Kronechker’s method, we extract the obtained minimal cost under form of an interval for a given solution. It allows us to obtain a goods allocation planning with the minimal total transportation cost.
Index Terms—Degeneration, point cloud, Pham’s method, fuzzy programming, fuzzy four index transportation problem.
Hoa Pham was with Hanoi University of Science and Technology, Hanoi, Vietnam and Clermont Auvergne University, Auvergne, France. She is now with R&D and Supply Chain Department, Engineer, Selecom Group, Clermont Ferrand, France (e-mail: tuyethoapham26675@gmail.com)
Fabien Escande was with Renault Group, Germany and France. He is now with R&D and Management Department, Chairman and CEO, Selecom Group, Clermont Ferrand, France (e-mail: f.escande@selecom.com)
Laurent Klupinski is with Supply Chain and Trade Department, Operation Director and Co-Leader, Selecom Group, Clermont Ferrand, France (e-mail: l.klupinski@selecom.com)
Cite: Hoa Pham, Fabien Escande, and Laurent Klupinski, "A New Approached Method for Solving the Four Index Transportation Problem with Fuzzy Parameters and Application Perspective in Industry," International Journal of Modeling and Optimization vol. 12, no. 4, pp. 142-149, 2022.
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